President Bush praised U.S. forces Wednesday for the raid Tuesday that killed Saddam Hussein's sons Uday and Qusay and also expressed joy for the Iraqi people now that they have further assurance the former regime is destroyed.

"Yesterday in the city of Mosul, the careers of two to the regime's chief henchman came to an end. Saddam Hussein's sons were responsible for the torture, maiming and murder of countless Iraqis. Now more than ever, all Iraqis can know the former regime is gone and will not be coming back," Bush said in a Rose Garden speech. He was flanked by Defense Secretary Donald Rumsfeld, Joint Chiefs of Staff Chairman Richard Myers and the U.S. administrator in Iraq Paul Bremer (search).

Bush said the deaths of Uday (search) and Qusay Hussein (search) mean nothing but good news for the war effort and he thanked Bremer for doing a "fine job" in helping reconstruct Iraq. Among the achievements, students are returning to school, a constitution is in the works and an Iraqi governing council has been appointed and recognized by U.N. Secretary-General Kofi Annan.

Bush let the Pentagon take the bows Tuesday for the 101st Airborne's raid on a Mosul villa that ended up killing the No. 2 and No. 3 most wanted Iraqis. The two were identified by multiple sources and dental records.

Officials said Bush was briefed Tuesday on the operation, but didn't need to sign off on the plans for it. He got a series of phone calls from Rumsfeld telling him first that Uday and Qusay might be dead and then that it had been confirmed. Officials said the White House was skeptical that the two were killed until it had been verified by the military.

On Tuesday, White House Press Secretary Scott McClellan released a statement talking about how horrible the Hussein brothers were to the people they were supposedly leading.

"Over the period of many years, these two individuals were responsible for countless atrocities committed against the Iraqi people and they can no longer cast a shadow of hate on Iraq," the statement read.

Bremer, who was briefing Congress when the confirmation was made, later said the deaths were welcomed by the Iraqi people.

"The fact that Baghdad was lighted up with celebratory gunfire tonight shows you how important this is in meeting the real desires of the Iraqi people to be rid once and for all of Saddam Hussein, his sons and his odious regime. This is important because it also shows the cooperation between the Iraqi's and the Americans."

Still, Iraqis want evidence that the "wolf" and the "snake," as they were known, are dead and won't return to torture them. In that regard, the military has said that they could release pictures of the two bodies.

And, U.S. forces are now on the hunt for Saddam Hussein. The ousted dictator appeared on another audiotape played on Arab television on Monday. Said to have been taped on Sunday, Saddam urges Iraqis to continue attacks on U.S. troops.

Indeed, attacks are continuing. Two more American soldiers were killed in Iraq overnight. They died during attacks on two convoys. U.S. soldiers in Iraq admit they are worried about revenge attacks. When Iraqi citizens celebrated in the streets with gunfire, a U.S. soldier shot a man and little girl by mistake, thinking troops were under attack.

Bush said that the United States will not allow "a few remaining holdouts" to stop the "advance of freedom."

"These killers are the enemies of Iraq's people. They operate mainly in a few areas of the country and wherever they operate, they are being hunted and they will be defeated," he said.

Bush added that a free Iraq will not be a training ground for terrorists.

"A free Iraq will not destabilize the Middle East, a free Iraq can set a hopeful example to an entire region," he said.

In Hong Kong, British Prime Minister Tony Blair, the U.S.'s closest ally in the war on terror and Operation Iraqi Freedom, called the killing of the two "monsters" great news.

"This is a great day for Iraq," Blair said. "These two particular people were the head of a regime ... that was responsible for the torture and killing of thousands and thousands of Iraqis."

Blair and Bush have both been under criticism for the use of questionable intelligence to make the case against war in Iraq. Tuesday's raid, which lasted six hours as U.S. troops slowly escalated their attack, blunted some of the criticism.

It also drowned out the latest White House admission about the president's State of the Union address in which National Security Adviser Condoleezza Rice's deputy admitted that he received two memos from the CIA calling into question the now-disputed intelligence.

Stephen Hadley said CIA Director George Tenet had also called him months before the address to warn that the intelligence about Iraq trying to buy uranium in Africa was too weak to rely on. Hadley said he should have remembered the exchanges before allowing the information to be included in the president's speech.

Bush aides said the president was upset by Hadley's failure to come forward with the CIA objections, but turned down what amounted to an offer by Hadley to resign.

Bush "has full confidence" in his national security team, including Hadley and Tenet, White House communications director Dan Bartlett said.

The White House acknowledged two weeks ago that the information they had was based on phony documents even though British intelligence, which forwarded the report, insists that they still have two other protected sources to verify the claim.

The White House has said the CIA's complaints to Hadley involved technical details only — where and how much uranium was sought — not a refutation of Iraq's attempts to buy the uranium.

Hadley said the memos warned all the evidence was weak and that the purchase wouldn't be worth much anyway.

Democrats called again for an investigation.

"These disclosures...raise more and more questions," said Sen. Carl Levin of Michigan, the top Democrat on the Senate Armed Services Committee.

Fox News' Wendell Goler and Jennifer Davis contributed to this report.